Constructing few-weight codes over finite fields is a long standing area of interest in algebraic coding theory. It has key applications in graph theory, finite geometry and combinatorial designs (see [1]}). The authors, in [2]} first introduced few-Lee weight codes over the finite ring \(\mathbb {F}_2+u\mathbb {F}_2\)  with \(u^2=0\)  and as an application they found some infinite families of optimal (with respect to the Griesmer bound) few-weight codes over \(\mathbb {F}_2\)  through Gray map. Apart from this, using a famous characterization of minimal codes, namely the Ashikhmin-Barg lemma, they showed that some of the Gray images are also minimal over \(\mathbb {F}_2\) , which have direct applications in secret sharing schemes and authentication codes (see [3]}, [4]}, [5]}, [6]}). Actually finding minimal codes over finite fields is itself a central topic in algebraic coding theory and in [2]} the authors succesfully clubbed these two important topics together. After that lots of researchers have constructed several classes of few-Lee weight codes over different finite chain rings of characteristic \(p\)  having optimal or minimal codes as appliactions. In particular for \(p=2\) , see [8]}, [9]}, [10]}, [11]}, [12]}, [13]}. The researchers mainly used suitable defining sets, simplicial complexes or down-sets(for \(p>2\)  only) to construct such codes (see [14]}, [15]}, [16]}). Very recently the authors in [17]} first studied few-Lee weight codes over a non-chain ring \(\mathbb {F}_2+u\mathbb {F}_2+v\mathbb {F}_2+uv\mathbb {F}_2\) .
